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List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes

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  • A list decoding algorithm for matrix-product codes is provided when $C_1, ..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.
    Mathematics Subject Classification: Primary: 94B05; Secondary: 94B35.


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